Solving schedulingandlocationproblemsintheplanesimultaneously

Inthispaperweconcentrateonthesimultaneoussinglemachinescheduling–location(ScheLoc) modelin the plane.Themodelcombinesboththelocationofthemachineandtheschedulingofthejobsexecuted bythemachine.Twoobjectivesareanalyzed:themakespanandthetotalcompletiontime.Basicproperties of themodelsareshownandlowerboundsonthevalueoftheobjectivefunctionsaredeveloped.Single machineScheLocproblemswithEuclidean,rectilinearandgeneral q normsaresolvedveryefficientlyby the “bigtrianglesmalltriangle”branch-and-boundapproach.Randomlygeneratedproblemswith10,000 jobsaresolvedinabout5–10minwithinarelativeaccuracyof = 10−5 fromtheglobaloptimum.